Question: Simplify the following expression: $z = \dfrac{3t^2 - 9t - 162}{t - 9} $
Answer: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $3$ , so we can rewrite the expression: $ z =\dfrac{3(t^2 - 3t - 54)}{t - 9} $ Then we factor the remaining polynomial: $t^2 {-3}t {-54} $ ${-9} + {6} = {-3}$ ${-9} \times {6} = {-54}$ $ (t {-9}) (t + {6}) $ This gives us a factored expression: $\dfrac{3(t {-9}) (t + {6})}{t - 9}$ We can divide the numerator and denominator by $(t + 9)$ on condition that $t \neq 9$ Therefore $z = 3(t + 6); t \neq 9$